If a vehicle's speed is doubled, what is the required stopping power?

When a vehicle's speed is doubled, the required stopping power increases by a factor of four. This is due to the physics of motion, specifically the relationship between speed, kinetic energy, and stopping distance.

Kinetic energy, which is the energy of a moving object, is calculated using the formula KE = ½ mv², where m is the mass of the vehicle and v is its speed. Thus, if you double the speed (v becomes 2v), the new kinetic energy becomes KE = ½ m(2v)², which simplifies to KE = ½ m(4v²). This shows that the kinetic energy—and therefore the stopping power needed—will actually increase by four times (4 times the original stopping power).

Additionally, stopping distance is related to the speed of the vehicle. If the speed of a vehicle doubles, the distance required to stop also increases, impacting the stopping power needed to bring the vehicle to a stop safely.

In summary, to effectively stop a vehicle whose speed has been doubled, you need four times the original stopping power.